Vector Components

Vector Components Based on the right angle triangle

Vector Components Θ Based on the right angle triangle Need a reference angle Θ

Vector Components Θ Based on the right angle triangle Need a reference angle Which sides are the adjacent, opposite, and hypotenuse? Θ

Vector Components Θ H A O Based on the right angle triangle Need a reference angle H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​? H H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​sinΘ H H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​sinΘ H O = ? H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​sinΘ H O = H sinΘ H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​sinΘ H O = H sinΘ Memorize this component equation #1 H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​sinΘ H O = H sinΘ Memorize this component equation #1 A = ? H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​sinΘ H O = H sinΘ Memorize this component equation #1 A = cosΘ H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​sinΘ H O = H sinΘ Memorize this component equation #1 A = cosΘ So A = ? H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​sinΘ H O = H sinΘ Memorize this component equation #1 A = cosΘ So A = H cosΘ H Θ A O

Vector Components Θ H A O Based on the right angle triangle Need a reference angle O = ​sinΘ H O = H sinΘ Memorize this component equation #1 A = cosΘ So A = H cosΘ Memorize component H equation #2 H Θ A O

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? Draw a vector component diagram.

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? Draw a vector component diagram. 300 km/h Θ=36.9° Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? Label A, O, H 300 km/h Θ=36.9° Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? Label A, O, H H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = component formula? H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ = 300.0 cos 36.9° H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ = 300.0 cos 36.9° = 240 H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ = 300.0 cos 36.9° = 240 O = component formula? H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ = 300.0 cos 36.9° = 240 O = H sinΘ H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ = 300.0 cos 36.9° = 240 O = H sinΘ = 300 sin 36.9° H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ = 300.0 cos 36.9° = 240 O = H sinΘ = 300 sin 36.9° = 180 H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ = 300.0 cos 36.9° = 240 O = H sinΘ = 300 sin 36.9° = 180 State the vector components using symbols with the XY plane as a reference axis. H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ = 300.0 cos 36.9° = 240 O = H sinΘ = 300 sin 36.9° = 180 Vx = +240 km/h = 240 km/h [ forward horizontal ] H 300 km/h O Θ=36.9° A Vector Component Diagram

Example #1: A plane takes off at 300. 0 km/h at an angle of 36 Example #1: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity? A = H cosΘ = 300.0 cos 36.9° = 240 O = H sinΘ = 300 sin 36.9° = 180 Vx = +240 km/h = 240 km/h [ forward horizontal ] Vy = +180 km/h = 180 km/h [ upward vertical ] H 300 km/h O Θ=36.9° A Vector Component Diagram

Harder Example #1b: A plane takes off at 300. 0 km/h at an angle of 36 Harder Example #1b: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. How many minutes does it take to reach an altitude of 3000.0 m? Vx = +240 km/h = 240 km/h [ forward horizontal ] Vy = +180 km/h = 180 km/h [ upward vertical ]

Harder Example #1b: A plane takes off at 300. 0 km/h at an angle of 36 Harder Example #1b: A plane takes off at 300.0 km/h at an angle of 36.9° to the ground. How many minutes does it take to reach an altitude of 3000.0 m? t = Δd/vy = 3000.0 m/ 180 km/h But 3000.0 m X 1 km/1000 m = 3.0000 km So t = 3.0000 km / 180 km/h or = 3.0000 km X (1/180 h/km) = 0.0167 h Convert to minutes t = 0.0167 h X 60 min/1 h = 1.00 minute

Try this example #2: What are the easterly and southerly components of the force 34.0 N [S28.1°E] ?

Try this example #2: What are the easterly and southerly components of the force 34.0 N [S28.1°E] ? A = H cosϴ = 34 cos 28.1° = 30.0 N O = H sinϴ = 34 sin 28.1° = 16.0 N Fx = +16.0 N = 16.0 N [East] Fy = - 30.0 N = 30.0 N [south] ϴ= 28.1° A 34.0 N O

Adding Vectors Using the Component Method

Adding Vectors Using the Component Method Can be used to add two or more vectors together

Adding Vectors Using the Component Method Can be used to add two or more vectors together Example: Find the vector sum of : 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] + 8.0 m/s [W]

Adding Vectors Using the Component Method Can be used to add two or more vectors together Example: Find the vector sum of : 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One

Adding Vectors Using the Component Method Can be used to add two or more vectors together Example: Find the vector sum of : 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors:

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors:

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, Find the vector components of any oblique vectors: 17 Θ=28.1°

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors: A = component formula? 17 Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ 17 Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, Find the vector components of any oblique vectors: A = H cosΘ = 17 cos(28.1°) 17 Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ = 17 cos(28.1°) = 15.0 17 Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ = 17 cos(28.1°) = 15.0 Symbol for west vector component? 17 Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, Find the vector components of any oblique vectors: A = H cosΘ = 17 cos(28.1°) = 15.0 vx= ? 17 Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ = 17 cos(28.1°) = 15.0 Vx= - 15.0 m/s 17 Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ O = formula? = 17 cos(28.1°) = 15.0 Vx= - 15.0 m/s 17 O=? Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, Find the vector components of any oblique vectors: A = H cosΘ O = H sinΘ = 17 cos(28.1°) = 15.0 Vx= - 15.0 m/s 17 O=? Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ O = H sinΘ = 17 cos(28.1°) = ? = 15.0 Vx= - 15.0 m/s 17 O=? Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ O = H sinΘ = 17 cos(28.1°) = 17sin(28.1°) = 15.0 Vx= - 15.0 m/s 17 O=? Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ O = H sinΘ = 17 cos(28.1°) = 17sin(28.1°) = 15.0 = 8.01 Vx= - 15.0 m/s 17 O=? Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ O = H sinΘ = 17 cos(28.1°) = 17sin(28.1°) = 15.0 = 8.01 Vx= - 15.0 m/s symbol for north component =? 17 O=? Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ O = H sinΘ = 17 cos(28.1°) = 17sin(28.1°) = 15.0 = 8.01 Vx= - 15.0 m/s Vy= ? 17 O=? Θ=28.1° A = ?

Adding Vectors Using the Component Method 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Step One: By drawing vector component diagrams, find the vector components of any oblique vectors: A = H cosΘ O = H sinΘ = 17 cos(28.1°) = 17sin(28.1°) = 15.0 = 8.01 Vx= - 15.0 m/s Vy= +8.01 m/s 17 O=? Θ=28.1° A = ?

Adding Vectors Using the Component Method Step One: Use vector component diagrams to find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s

Adding Vectors Using the Component Method Step One By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s 22.6° 13

Adding Vectors Using the Component Method Step One: By drawing vector component diagrams,find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = component formula? 22.6° 13 A=?

Adding Vectors Using the Component Method Step One: By drawing vector component diagrams,find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ 22.6° 13 A=?

Adding Vectors Using the Component Method Step One: By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ = 13cos(22.6°) 22.6° 13 A=?

Adding Vectors Using the Component Method Step One: By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ = 13cos(22.6°) = 12.0 22.6° 13 A=?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ = 13cos(22.6°) = 12.0 Symbol for south vector component? 22.6° 13 A=?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ = 13cos(22.6°) = 12.0 Vy = ? 22.6° 13 A=?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ = 13cos(22.6°) = 12.0 Vy = - 12.0 m/s 22.6° 13 A=?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ O = formula ? = 13cos(22.6°) = 12.0 Vy = - 12.0 m/s 22.6° 13 A=? O =?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ O = HsinΘ = 13cos(22.6°) = 12.0 Vy = - 12.0 m/s 22.6° 13 A=? O =?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ O = HsinΘ = 13cos(22.6°) = 13sin(22.6°) = 12.0 Vy = - 12.0 m/s 22.6° 13 A=? O =?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ O = HsinΘ = 13cos(22.6°) = 13sin(22.6°) = 12.0 = 5.00 Vy = - 12.0 m/s 22.6° 13 A=? O =?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ O = HsinΘ = 13cos(22.6°) = 13sin(22.6°) = 12.0 = 5.00 Vy = - 12.0 m/s symbol for east vector component ? 22.6° 13 A=? O =?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ O = HsinΘ = 13cos(22.6°) = 13sin(22.6°) = 12.0 = 5.00 Vy = - 12.0 m/s Vx= ? 22.6° 13 A=? O =?

Adding Vectors Using the Component Method Step One : By drawing vector component diagrams, find the vector components of any oblique vectors 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vy= +8.01 m/s A = HcosΘ O = HsinΘ = 13cos(22.6°) = 13sin(22.6°) = 12.0 = 5.00 Vy = - 12.0 m/s Vx= +5.00 m/s 22.6° 13 A=? O =?

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= ? Vx= ? Vy= +8.01 m/s Vy = - 12.0 m/s Vy= ? Vy= ?

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= ? Vy= +8.01 m/s Vy = - 12.0 m/s Vy= ? Vy= ?

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= ? Vy= +8.01 m/s Vy = - 12.0 m/s Vy= ? Vy= ?

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= ? Vy= +8.01 m/s Vy = - 12.0 m/s Vy= -10.0 m/s Vy= ?

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= -8.0 m/s Vy= +8.01 m/s Vy = - 12.0 m/s Vy= -10.0 m/s Vy= ?

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= -8.0 m/s Vy= +8.01 m/s Vy = - 12.0 m/s Vy= -10.0 m/s Vy= 0.m/s

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= -8.0 m/s Vy= +8.01 m/s Vy = - 12.0 m/s Vy= -10.0 m/s Vy= 0.m/s Step Three: Add the x components and y components

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= -8.0 m/s Vy= +8.01 m/s Vy = - 12.0 m/s Vy= -10.0 m/s Vy= 0.m/s Step Three: Add the x components and y components Vx (total) = ? Vy (total) = ?

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= -8.0 m/s Vy= +8.01 m/s Vy = - 12.0 m/s Vy= -10.0 m/s Vy= 0.m/s Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = ?

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= -8.0 m/s Vy= +8.01 m/s Vy = - 12.0 m/s Vy= -10.0 m/s Vy= 0.m/s Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= -8.0 m/s Vy= +8.01 m/s Vy = - 12.0 m/s Vy= -10.0 m/s Vy= 0.m/s Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: ?

Adding Vectors Using the Component Method Step Two: Set up a chart listing the x and y components 17.0 m/s [W28.1°N] + 13.0 m/s [S22.6°E] + 10.0 m/s [S] +8.0 m/s [W] Vx= - 15.0 m/s Vx= +5.00 m/s Vx= 0 m/s Vx= -8.0 m/s Vy= +8.01 m/s Vy = - 12.0 m/s Vy= -10.0 m/s Vy= 0.m/s Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes 18.0 m/s

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes 18.0 m/s 14.0 m/s

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes 18.0 m/s 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ? 18.0 m/s 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ( 18.02 + 14.02 )1/2 18.0 m/s 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ( 18.02 + 14.02 )1/2 = 22.8 m/s 18.0 m/s 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ( 18.02 + 14.02 )1/2 = 22.8 m/s Where is the reference angle? 18.0 m/s 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ( 18.02 + 14.02 )1/2 = 22.8 m/s Where is the reference angle? 18.0 m/s Θ 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ( 18.02 + 14.02 )1/2 = 22.8 m/s Θ = ? 18.0 m/s Θ 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ( 18.02 + 14.02 )1/2 = 22.8 m/s Θ = Tan-1 ( 14.0/18.0 ) don't sub negatives 18.0 m/s Θ 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ( 18.02 + 14.02 )1/2 = 22.8 m/s Θ = Tan-1 ( 14.0/18.0 ) don't sub negatives = 37.9° 18.0 m/s Θ 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ( 18.02 + 14.02 )1/2 = 22.8 m/s Θ = Tan-1 ( 14.0/18.0 ) don't sub negatives = 37.9° Vtotal = ? 18.0 m/s Θ 14.0 m/s Vector sum or Vtotal

Adding Vectors Using the Component Method Step Three: Add the x components and y components Vx (total) = -18.0 m/s Vy (total) = -14.0 m/s Step Four: Draw a tip-to-tail diagram and find the vector sum Note: Just label as positive magnitudes | Vtotal | = ( 18.02 + 14.02 )1/2 = 22.8 m/s Θ = Tan-1 ( 14.0/18.0 ) don't sub negatives = 37.9° Vtotal = 22.8 m/s [ W37.9°S] or [S52.1°W] 18.0 m/s Θ 14.0 m/s Vector sum or Vtotal

Try this: Add these vectors using the component method: 12. 0 m [E25 Try this: Add these vectors using the component method: 12.0 m [E25.0° S] + 14.0 m [N38.0°W] + 11.0 m [S]

Try this: Add these vectors using the component method: 12. 0 m [E25 Try this: Add these vectors using the component method: 12.0 m [E25.0° S] + 14.0 m [N38.0°W] + 11.0 m [S] A A = HcosΘ O = HsinΘ = 12.0cos25.0° = 12.0 sin 38.0° = 10.9 = 5.07 Δdx = +10.9 m Δdy = -5.07 m A = HcosΘ O = HsinΘ = 14cos38° = 14sin38° = 11.0 = 8.62 Δdx = - 8.62 m Δdy = + 11.0 m Chart Δdx (total) = +10.9 m - 8.62 m + 0 m = 2.3 m Δdy (total) = -5.07 m +11.0 m -11.0 m = -5.1 m 25.0° O H = 12 O H = 14 A 38.0°

Try this: Add these vectors using the component method: 12. 0 m [E25 Try this: Add these vectors using the component method: 12.0 m [E25.0° S] + 14.0 m [N38.0°W] + 11.0 m [S] Chart Δdx (total) = +10.9 m - 8.62 m + 0 m = 2.3 m Δdy (total) = -5.07 m +11.0 m -11.0 m = -5.1 m Tip-to-tail |Δdtotal | = ( 5.12 + 2.32 )1/2 = 5.6 m θ = tan-1(O/A) = tan-1(5.1/2.3) = 66° Δdtotal = 5,6 m [E66°S] or [S24°E] 2.3 Θ 5.1 Δdtotal No negatives